Robust Adaptive Fuzzy Control For A Class Of Nonlinear Systems Based On Observer

In practice, it's very difficult to get the precise mathematical model from the traditional modeling method. Fuzzy systems with a collection of fuzzy IF-THEN, rules are capable of approximating any real continous function on a compact set with arbitrary accuracy. Because of not requiring precise mathematical models, fuzzy control has successfully applied to many control problems.In addition, the recent study of adaptive fuzzy control has developed quickly. In many design problems, all states of systems are supposed to be available for measurement. But in practice, that not all states are available for measurement.The robust indirect and direct adaptive fuzzy control methods are proposed for a class of nonlinear systems based on observer in this paper, respectively. The main content has two parts: In the fist part, we design the state observer to estimate the unknown state, and advance the scheme of robust indirect adaptive fuzzy making use of the H_∞ control theory and the characteristic of fuzzy logic is universal approximation. Finally, we prove that the states of the closed loop systems are uniformly bounded and the tracking error is attenuated to an arbitrarily desired level via H_∞ tracking design technique. In the second part, we design the robust direct adaptive fuzzy controller with the ability of supervisory, based on a kind of revised scheme of supervisory control, for a nonlinear uncertain and perturbed and modeling error system. If the fuzzy control system can maintain the stability, the supervisory controller stops working. On the contrary, if the fuzzy control cannot maintain stability, the supervisory controller starts working to guarantees stability. The adaptive law has gained from the Lyapunov synthesize method and design procedure. Finally, we demonstrate the effectiveness of the proposed method by simulation results.